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Monday, August 03, 2015

Every spring, graduating medical students in the United States stress out in the middle of March over the results of the the National Residency Matching Program (NRMP), generally celebrated by medical school as "Match Day." No other profession operates like this. Lawyers after law school, PhDs after graduate school, MBAs after business school - all enter a competitive job market. Medicine instead has a nationalized system that ostensibly relies on de jure collusion between residency programs to assure a reasonable allocation of residents to programs on a predictable schedule. How did this come to be?

The History of The Match
In the United States prior to 1952, medical students found residency positions much like their colleagues in other fields, through a decentralized, competitive market. However, as residency programs wanted the best residents, they often competed to offer spots earlier and earlier to the brightest candidates, causing undue stress. As Sara Robinson writes:

Medical internships were introduced around the turn of the last century as an optional form of postgraduate education. Because
interns were a source of cheap labor for hospitals, Roth explains, slots soon outnumbered applicants and competition for interns
was fierce.
Salaries and working conditions of the internships were specified ahead of time, even then, and there was no negotiation in the
process. Thus, the competition manifested itself in timing rather than price: Hospitals began to insist that their offers be finalized
before those of their competitors.
The average date for finalizing an internship gradually crept from the end to the beginning of the senior year. By the mid-1940s,
internships were being finalized at the beginning of the junior year of medical school, and some inquiries came even during the
sophomore year.

Recognizing that the situation was out of hand, the Association of American Medical Colleges adopted a resolution prohibiting
medical schools from disseminating student transcripts or reference letters before a certain date during the senior year. This fixed
the advancing-date problem but created a new one: Students tended to hold onto offers as long as possible, hoping for offers from
better schools.
The hospitals were unhappy with this situation; if a student rejected an offer at the last moment, the hospital might have trouble
filling the slot with a desirable applicant. So the hospitals, still battling fiercely for residents, passed a series of resolutions
shortening the time a student could sit on an offer. At one point, hospitals had telegrams offering residency positions delivered at
precisely 12:01 A.M. on the earliest allowed day; the students were forced to accept or reject these offers within hours.

In response to this clearly unsustainable situation, all parties decided, in the early 1950s, that it was time for drastic changes in
the procedure. The centralized system created as a result had students and hospitals communicating with each other as before, but
it replaced the rounds of offers by ranking lists, submitted by both sides to a central authority. Following a standard procedure, the
central authority then matched students with residency programs. Such was the inception of the residency-matching algorithm,
although it took some fiddling (trial and error) to get a procedure that worked.

The situation improved, although economists and game theorists argued that the situation favored the hospitals.

The NRMP Algorithm

In general, the problem of matching residents to programs is one of two-sided matching, or more amusingly called the "Stable Marriage Problem." The basic problem is stated as:

Imagine a set of n boys and n girls. Each boy B ranks each girl G, and vice versa. The first boy goes to his preferred girl and proposes. If he is on the top of her list, she says 'Maybe' (for now); otherwise, she says 'No.' If she says no, he goes on to his next choice, until he finally gets to a 'maybe.' Then, the next boy repeats the same process with the remaining girls, which goes on until all the boys have paired off with all the girls.

The original research showed that while this produces a stable set of pairs such that no improvements can be made by any couple re-pairing (ie, no cheating), it was also shown that this process favors the boys (the ones asking) over the girls. Another implication was that the girls could game the system by lying about their true preferences. Economist Alvin Roth and others showed that the original NRMP algorithm was equivalent to the stable marriage problem and that it favored the hospitals. In the 1990s, Roth was recruited by the NRMP to revise its algorithm as well as make it more equitable for couples entering the match.

Despite these changes, several medical students filed an anti-trust lawsuit against the NRMP in 2002, accusing it of abetting medical schools in colluding to keep wages low. The suit was unsuccessful, but the lobbying efforts of the NRMP fared better: President Bush signed a pension law that had an attached rider specifically granting immunity to the NRMP from such claims in 2004.

Navigating the Match
In an ideal world, simply putting down your true preferences and having the residency programs do the same would lead to optimal outcomes. In reality, the process entails much subjectivity as programs want not only qualified applicants but also want to claim they did not have to go very far down their list to fill their spots. This is more an issue of vanity than practicality, but it impacts how programs structure their rank lists. Awareness of this social reality behooves the applicant to clearly state their desires for programs they are interested in during the interview process, despite not having fully considered all their options. It also necessitates clear communication with programs of interest after the formal interviews in order to ascertain if the feeling is mutual. While the degree of communication between applicants and programs is restricted per the NRMP guidelines, if any programs or applicants deviate, it is in the best interests of each applicant to also deviate (to understand this better, check out the prisoner's dilemma). Ultimately, the applicant should take whatever steps necessary to clarify his preferences with programs of interest.

If you are interested in learning more about how to navigate the match, check out: